Michael Tsatsomeros

  Professor

  Office: Neill Hall 229

  Phone: (509) 335-3144

  Fax: (509) 335-1188

  Email: tsat at wsu.edu

Quick links:
[PUBLICATIONS]   [PRESENTATIONS]   [MATLAB DEPOT] 
[INTERNATIONAL LINEAR ALGEBRA SOCIETY]   [WSU COUGARS SPORTS]

Education

• Ph.D., Mathematics, University of Connecticut - 1990
  Supervisor: Michael Neumann (In Memoriam)
  
• M.Sc., Mathematics, Concordia University, Montreal - 1986
  Supervisor: Ronald J. Stern - Here's a copy of my thesis
  
• Diploma, Mathematics, University of Patras, Greece - 1984

Research Interests

Linear algebra, matrix analysis, especially the theory of nonnegative matrices and their generalizations. Particular interests include the numerical range; graphs and patterns associated with matrices; numerical linear algebra; applications in dynamical systems, control theory, data analysis, machine learning and artificial intelligence.

Work Experience

• 2007 - present, Professor, Washington State University, Pullman, WA
• 2001-07, Associate Professor, Washington State University
• 1997-2002, Associate Professor, University of Regina, Saskatchewan, Canada
• 1994-97, Assistant Professor, University of Regina
• 1993-94, Adjunct Assistant Professor, University of Regina
• 1993, Visiting Assistant Professor, College of William and Mary, Williamsburg, VA
• 1992, Visiting Assistant Professor, University of Wisconsin, Madison, WI
• 1990-92, Post-doctoral Fellow, University of Victoria, British Columbia, Canada

Supervision

• Seong Park, Jesse Lopez, Ben Clark, Allison Roberson, Samir Mondal (IITM)

• Wail Alahmadi (Ph.D. 2023)
  Thesis tittle: Convex Sets of Stable Matrices
• Sushmitha Parameswaran (co-Chair with K.C. Sivakumar, Ph.D., IIT Madras, 2021)
  Thesis title: On Some Generalizations of the Class of Q-Matrices
• Hung Le (Ph.D. 2020)
  Thesis title: Matrix Analysis Primer for Inhomogeneous Markov Chains
• Faith Zhang (Ph.D., 2020)
  Thesis title: Rank One Perturbations and Applications
• Megan Wendler (Ph.D., 2020)
  Thesis title: Semimonotone Matrices
• Patrick Torres (Ph.D., 2018)
  Thesis title: Stability Analysis, Convex Hulls of Matrix Powers and Their Relations to P-matrices
• Michael Kasigwa (Ph.D., 2017)
  Thesis title: Eventual Cone Invariance
• Thomas Cameron (Ph.D., 2016)
  Thesis title: On the Computation of Eigenvalues, Spectral Bounds and Hessenberg Form of Matrix Polynomials
• Pietro Paparella (Ph.D., 2013, co-supervised with J.J. McDonald)
  Thesis title: Matrix Roots of Nonnegative and Eventually Nonnegative Matrices
• Jimmy Burk (Ph.D., 2012)
  Thesis title: Eigenspaces of Tournament Matrices
• Kent Griffin (Ph.D., 2006)
  Thesis title: Solving the Principal Minor Assignment Problem and Related Computations
• Bishan Li (Ph.D., Univ. of Regina, 1998)
  Thesis title: Generalizations of Diagonal Dominance in Matrix Theory

• Fei Zhou (Post-doctoral fellow, 2006)
• Panos Psarrakos (Post-doctoral fellow, 2000)
  Currently: Professor, Mathematics, National Technical University of Athens
• Mark Krupnik (Post-doctoral fellow, 1994-1995)
  Currently: Retalon, Inc (inventory management and forecasting tools), Co-founder and President

Grants/Awards

• Excellence in Graduate Advising and Mentoring, College of Arts and Sciences, WSU, 2021
• SPARC Indian Institure of Technology-Madras Collaboration Grant, 2019-2021
• Outstanding Research Award, Mathematics, WSU, 2007
• Catalyzing the Future Award, WSU, 2003
• NSERC Research Grants: 1994-1997, 1997-2001, 2001-2002
• NSERC Equipment Grants: 1994, 1996, 2001
• Merit Awards, Univ. of Regina, 1996, 1999

Books

• Panayiotis J. Psarrakos and Michael J. Tsatsomeros.
  Linear Algebra and Matrix Methods. Cognella, San Diego, 2024.
• Charles R. Johnson, Ronald L. Smith, and Michael J. Tsatsomeros.
  Matrix Positivity. Cambridge University Press, 2020.

Publications (in reverse chronological order)

• Samir Mondal, K.C. Sivakumar, and M.J. Tsatsomeros.
  The Cayley Transform of Prevalent Matrix Classes.
  Linear Algebra and its Applications, 681:1-20, 2024.


• Samir Mondal, K.C. Sivakumar, and M.J. Tsatsomeros.
  New Results on M-matrices, H-matrices and their Inverse Classes.
  Electronic Journal of Linear Algebra, 38:729-744, 2022.


• Hung V. Le and M.J. Tsatsomeros
  Matrix Analysis for Continuous-Time Markov Chains.
  Special Matrices, 10:219-233, 2022.


• Michael J. Tsatsomeros and Yueqiao Faith Zhang.
  Recursive Rank One Perturbations for Pole Placement and Cone Reachability.
  Applied Mathematics and Computation, Vol. 416, Issue C, March 2022.
• K.C. Sivakumar, P. Sushmitha, and M.J. Tsatsomeros.
  Q_#-Matrices and Q_†-Matrices: Two Extensions of the Q-Matrix Concept.
  Linear and Multilinear Algebra, 70(21):6947-6964, 2022.

• Michael J. Tsatsomeros and Yueqiao Faith Zhang.
  The Fiber of P-matrices: The Recursive Construction of All Matrices with Positive Principal Minors.
  Linear and Multilinear Algebra, 69:224-232, 2021.

• J.J. McDonald, R. Nandi, K.C. Sivakumar, P. Sushmitha, M.J. Tsatsomeros, Enzo Wendler, and Megan Wendler.
  M-matrix and Inverse M-matrix Extensions.
  Special Matrices, 8:186-203, 2020.

• Charles R. Johnson, Ronald L. Smith, and Michael J. Tsatsomeros.
  Matrix Positivity. Cambridge University Press, 2020.

• Projesh Nath Choudhury and Michael J. Tsatsomeros.
  Algorithmic Detection and Construction of N-matrices.
  Linear Algebra and Its Applications, 602:46-56, 2020.

• Michael J. Tsatsomeros and Megan Wendler.
  Semimonotone Matrices.
  Linear Algebra and Its Applications, 578:207-224, 2019.

• P.K. Torres and M.J. Tsatsomeros.
  Stability and Convex Hulls of Matrix Powers.
  Linear and Multilinear Algebra, 66(4):769-775, 2018.

• K.C. Sivakumar and M.J. Tsatsomeros.
  Semipositive Matrices and Their Semipositive Cones.
  Positivity, 22(1):379-398, 2018.

• Ik-Pyo Kim and M.J. Tsatsomeros.
  Inverse Relations in Shapiro's Open Questions
  Discrete Mathematics, 341:691-700, 2018.

• Ik-Pyo Kim and M.J. Tsatsomeros.
  Pascal Eigenspaces and Invariant Sequences of the First or Second Kind.
  Linear Algebra and its Applications, 535:171-190, 2017.

• Aik. Aretaki, P. Psarrakos, and M. Tsatsomeros.
  The Envelope of Tridiagonal Toeplitz Matrices and Block-Shift Matrices.
  Linear Algebra and its Applications, 532:60-85, 2017.

• M. Kasigwa and M.J. Tsatsomeros.
  Eventual Cone Invariance.
  Electronic Journal of Linear Algebra, 32:204-216, 2017.

• M.J. Tsatsomeros.
  Geometric Mapping Properties of Semipositive Matrices.
  Linear Algebra and its Applications, 498:349-359, 2016.

• P. Psarrakos and M.J. Tsatsomeros.
  On the Geometry of the Envelope of a Matrix.
  Applied Mathematics and Computation, 244:132-141, 2014.

• J.J. McDonald, P. Paparella, and M.J. Tsatsomeros.
  Matrix Roots of Eventually Positive Matrices.
  Linear Algebra and its Applications, 456:122-137, 2014.

• M. Cavers, S.M. Cioaba, S. Fallat, D.A. Gregory, W. Haemers, S.J. Kirkland, J.J. McDonald, and M. Tsatsomeros.
  Skew-Adjency Matrices of Graphs.
  Linear Algebra and its Applications, 436:512-4529, 2012.

• D.D. Olesky, M.J. Tsatsomeros, and P. van den Driessche.
  Sign Patterns with a Nest of Positive Principal Minors.
  Linear Algebra and its Applications, 436:4392-4399, 2012.

• J. Burk and M.J. Tsatsomeros.
  On the Brualdi-Li Matrix and its Perron Eigenspace.
  Electronic Journal of Linear Algebra, 23:212-230, 2012.

• P. Psarrakos and M.J. Tsatsomeros.
  An Envelope for the Spectrum of a Matrix.
  Central European Journal of Mathematics, 10:292-302, 2012.

• Michael Tsatsomeros.
  In Memoriam: Michael (Miki) Neumann (1946-2011).
  Linear Algebra and its Applications, 436:1-11, 2012.

• George Psarrakos and Michael Tsatsomeros.
  Ratio Monotonicity for Tail Probabilities in the Renewal Risk Model.
  Probability in the Engineering and Informational Sciences., 25:171-185, 2011.

• A. Berman, M. Catral, L.M. DeAlba, A. Elhashash, F.J. Hall, L. Hogben, I.-J. Kim, D.D. Olesky, P. Tarazaga, M.J. Tsatsomeros, and P. van den Driessche.
  Sign Patterns that Allow Eventual Positivity
  Electronic Journal of Linear Algebra, 19:108-120, 2009/2010.

• E. Ellison, L. Hogben, and M. Tsatsomeros.
  Sign Patterns that Require Eventual Positivity or Require Eventual Nonnegativity.
  Electronic Journal of Linear Algebra, 19:98-107, 2009/2010.

• D.D. Olesky, M.J. Tsatsomeros, and P. van den Driessche.
  Mv - Matrices : A Generalization of M-matrices Based on Eventually Nonnegative Matrices.
  Electronic Journal of Linear Algebra, 18:339-351, 2009.

• D. Noutsos and M. Tsatsomeros.
  On the Numerical Characterization of the Reachability Cone for an Essentially Nonnegative Matrix.
  Linear Algebra and its Applications, 430(4):1350-1363, 2009.

• K. Griffin, J. Stuart, and M. Tsatsomeros.
  Noncirculant Toeplitz Matrices All of Whose Powers are Toeplitz.
  Chzechoslovak Mathematical Journal, 58(4):1185-1193, 2008.

• D. Noutsos and M.J. Tsatsomeros.
  Reachability and Holdability of Nonnegative States
  SIAM Journal on Matrix Analysis and Applications, 30(2):700-712, 2008.

• O. Slyusareva and M. Tsatsomeros.
  Mapping and Preserver Properties of the Principal Pivot Transform.
  Linear and Multilinear Algebra, 56(3):279-292, 2008.

• K. Griffin and M. Tsatsomeros.
  Principal Minors, Part I: A Method for Computing All the Principal Minors of a Matrix.
  Linear Algebra and its Applications, 419:107-124, 2006.

• K. Griffin and M. Tsatsomeros.
  Principal Minors, Part II: The Principal Minor Assignment Problem.
  Linear Algebra and its Applications, 419:125-171, 2006.

  The software associated with the above two papers can be found here.

• M. Adam and M.J Tsatsomeros.
  An Eigenvalue Inequality and Spectrum Localization fo Complex Matrices.
  Electronic Journal of Linear Algebra, 15:239-250, 2006.

• P. Psarrakos and M. Tsatsomeros.
  Bounds for Levinger's Function of Nonnegative Almost Skew-symmetric Matrices.
  Linear Algebra and its Applications, 416:759-772, 2006.

• R.Edwards, J.J. McDonald, and M.J. Tsatsomeros.
  On Matrices with Common Invariant Cones with Applications to Neural and Gene Networks.
  Linear Algebra and its Applications, 398:37-67, 2005.

• V. Monov and M. Tsatsomeros.
  On Reducing and Deflating Subspaces of Matrices.
  Electronic Journal of Linear Algebra, 11 : 246-257, 2004.

• P.J. Psarrakos and M.J. Tsatsomeros.
  A Primer of Perron-Frobenius Theory for Matrix Polynomials.
  Linear Algebra and its Applications, 393:333-352, 2004.

• V. Monov and M. Tsatsomeros.
  A Criterion for Reducibility of Matrices.
  Cybernetics and Information Technologies, 4(2):60--68, 2004.
   
• J.J. McDonald, P.J. Psarrakos and M.J. Tsatsomeros.
  Almost Skew-Symmetric Matrices.
  Rocky Mountain Journal of Mathematics, 34:269-288, 2004.

• M. Tsatsomeros.
  Generating and Detecting Matrices with Positive Principal Minors.
  In Focus on Computational Neurobiology, Lei Li, Editor, pp. 115-132, Nova Science, New York, 2004.

• P.J. Psarrakos and M.J. Tsatsomeros.
  The Perron Eigenspace of Nonnegative Almost Skew-Symmetric Matrices and Levinger's Transformation.
  Linear Algebra and its Applications, 360:43-57, 2003.

• J.J. McDonald, D.D. Olesky, M.J. Tsatsomeros, and P. van den Driessche.
  On the Spectra of Striped Sign Patterns.
  Linear and Multilinear Algebra, 51:39-48, 2003.

• P.J. Psarrakos and M.J. Tsatsomeros.
  Numerical Range: (in) a Matrix Nutshell, Parts 1 / 2.
  Mathematical Notes from Washington State University, Vol 45, No. 2, 2002 / Vol 46, No. 1, 2003.

• S.M. Fallat and M.J Tsatsomeros.
  On the Cayley Transform of Positivity Classes of Matrices.
  Electronic Journal of Linear Algebra, 9:190-196, 2002.

• P.J. Psarrakos and M.J. Tsatsomeros.
  On the Stability Radius of Matrix Polynomials.
  Linear and Multilinear Algebra, 50 : 151-165, 2002.

• J. Maroulas, P.J. Psarrakos, and M.J. Tsatsomeros.
  Perron-Frobenius Type Results on the Numerical Range.
  Linear Algebra and its Applications, 348 : 49-62, 2002.

• S. Kirkland, P.J. Psarrakos, and M.J. Tsatsomeros.
  On the Location of the Spectrum of Hypertournament Matrices.
  Linear Algebra and its Applications, 323 : 37-49, 2001.

• M. Tsatsomeros.
  A Criterion for the Existence of Common Invariant Subspaces of Matrices.
  Linear Algebra and its Applications, 322 : 51-59, 2001.

• T. Myers and M. Tsatsomeros.
  Potash Crystallization.
  Report in the Proceedings of the 1st Prairie Industrial Problem Solving Workshop,
  August 7-11, 2000, Brandon, Manitoba.

• J. Maroulas, P.J. Psarrakos, and M.J. Tsatsomeros.
  Separable Characteristic Polynomials of Pencils and Property L.
  Electronic Journal of Linear Algebra, 7 : 182-190, 2000.

• G.Y. Lee, J.J. McDonald, B.L. Shader, and M.J. Tsatsomeros.
  Extremal Properties of Ray-nonsingular Matrices.
  Discrete Mathematics, 216 : 221-233, 2000.

• M. Tsatsomeros.
  Principal Pivot Transforms: Properties and Applications.
  Linear Algebra and its Applications, 307 : 151-165, 2000.

• M. Tsatsomeros and L. Li.
  A Recursive Test for P-Matrices.
  BIT Numerical Mathematics, 40(2) : 410-414, 2000.

• P. J. Psarrakos and M. J. Tsatsomeros.
  On the Relation Between the Numerical Range and the Joint Numerical Range of Matrix Polynomials.
  Electronic Journal of Linear Algebra, 6 : 20-30, 2000.

• L. Han, M. Neumann, and M. Tsatsomeros.
  Spectral Radii of Fixed Frobenius Norm Perturbations of Nonnegative Matrices.
  SIAM Journal on Matrix Analysis and Applications, 21 : 79-92, 1999.

• J.J. McDonald, R. Nabben, M. Neumann, H. Schneider, and M. Tsatsomeros.
  Inverse Tridiagonal Z-Matrices.
  Linear and Multilinear Algebra, 45 : 75-97, 1998.

• J.J. McDonald, D.D. Olesky, H. Schneider, M.J. Tsatsomeros, and P. van den Driessche.
  Z-Pencils.
  Electronic Journal of Linear Algebra, 4 : 32-38, 1998.

• M. Tsatsomeros.
  Sign Controllability: Sign Patterns That Require Complete Controllability.
  SIAM Journal on Matrix Analysis and Applications, 19 : 355-364, 1998.

• B. Li, L. Li, M. Harada, H. Niki, and M. Tsatsomeros.
  An Iterative Criterion for H-matrices.
  Linear Algebra and Its Applications, 271 : 179-190, 1998.

• J.J. McDonald, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
  Ray Patterns of Matrices and Nonsingularity.
  Linear Algebra and its Applications, 267 : 359-373, 1997.

• B. Li and M. Tsatsomeros.
  Doubly Diagonally Dominant Matrices.
  Linear Algebra and its Applications, 261 : 221-235, 1997.

• S. Kirkland, J.J. McDonald, and M. Tsatsomeros.
  Sign Patterns that Require Positive Eigenvalues.
  Linear and Multilinear Algebra, 41 : 199-210, 1996.

• J.J. McDonald, M. Neumann, H. Schneider, and M. Tsatsomeros.
  Inverses of Unipathic M-Matrices.
  SIAM Journal on Matrix Analysis and Applications, 17 : 1025-1036, 1996.

• C.R. Johnson, M. Neumann, and M. Tsatsomeros.
  Conditions for the Positivity of Determinants.
  Linear and Multilinear Algebra, 40 : 241-248, 1996.

• C.R. Johnson and M. Tsatsomeros.
  Convex Sets of Nonsingular and P-Matrices.
  Linear and Multilinear Algebra, 38 : 233-239, 1995.

• J.J. McDonald, M. Neumann, H. Schneider, and M. Tsatsomeros.
  Inverse M-Matrix Inequalities and Generalized Ultrametric Matrices.
  Linear Algebra and its Applications, 220 : 321-341, 1995.

• C.R. Johnson, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
  An Identity for the Determinant.
  Linear and Multilinear Algebra, 36 : 189-194, 1994.

• D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
  Qualitative Controllability and Uncontrollability by a Single Entry.
  Linear Algebra and its Applications, 187 : 183-194, 1993.

• M. Tsatsomeros, J.S. Maybee, D.D. Olesky, and P. van den Driessche.
  Nullspaces of Matrices and Their Compounds.
  Linear and Multilinear Algebra, 34 : 291-300, 1993.

• C.R. Johnson, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
  Spectra with Positive Elementary Symmetric Functions.
  Linear Algebra and its Applications, 180 : 247-262, 1993.

• J.S. Maybee, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
  Combinatorial Eigenvalues of Matrices.
  Linear Algebra and its Applications, 175 : 213-224, 1992.

• M. Neumann and M. Tsatsomeros.
  Symbiosis Points for Linear Differential Systems.
  Linear and Multilinear Algebra, 30 : 49-59, 1991. [References]

• M. Neumann, R.J. Stern, and M. Tsatsomeros.
  The Reachability Cones of Essentially Nonnegative Matrices.
  Linear and Multilinear Algebra, 28 : 213-224, 1991. [References]

• R.J. Stern and M. Tsatsomeros.
  Extended M-Matrices and Subtangentiality.
  Linear Algebra and its Applications, 97 : 1-11, 1987.

• Envelope: Localizaton of the Spectrum of a Matrix Envelope: Localization of the Spectrum of a Matrix (NASCA, Kalamata 2018)
• Lecture notes on P-matrices   (GIAN Course, Indian Institute of Technology - Madras, 2017)
• Perron-Frobenius Theory and Positivity in Linear Algebra (in honour of Hans Schneider)   (ALA, Novi Sad 2010)
• Spectrum localization for almost skew-symmetric matrices   (BIRS, Banff 2003)
• Generating and detecting matrices with positive principal minors   (ILAS, Auburn 2002)
• Since Ancient Greece   (A power point presentation on two "modern" era Greek mathematicians)

Current Editorship

• Advisory Editor (past Co-Editor-In-Chief) of Electronic Journal of Linear Algebra
• Associate Editor of Linear Algebra and its Applications

• Linear Algebra and its Applications, Vol 341, Issues 1-3, pp. 1-420, 2002
  Dedicated to Tsuyoshi Ando in recognition of his 70th birthday.
• Linear Algebra and its Applications, Vol. 393, pp. 1-432, 2004.
  Dedicated to Positivity in Linear Algebra.
• Linear Algebra and its Applications. Vol. 409, pp. 1-187, 2005.
  Dedicated to Pauline van den Driessche.
• Electronic Journal of Linear Algebra , Vol. 19, pp. 1-140, 2009/2010.
  On the occasion of the AIM workshop Nonnegative Matrix Theory: Generalizations and Applications.
• Linear Algebra and its Applications. Vol. 436, 2012.
  Dedicated to the Applied Linear Algebra Conference held in Novi Sad in 2010.